Related papers: Stein's method for the matrix normal distribution
We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…
We provide explicit bounds on the Wasserstein distance between discrete time martingales and the standard normal distribution. The proofs are based on a combination of Lindeberg's and Stein's method.
We develop connections between Stein's approximation method, logarithmic Sobolev and transport inequalities by introducing a new class of functional inequalities involving the relative entropy, the Stein kernel, the relative Fisher…
The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
In this paper, we obtain quantitative, non-asymptotic, and data-dependent \textit{Bernstein-von Mises type} bounds on the normal approximation of the posterior distribution in exponential family models with arbitrary centring and scaling.…
Let $M$ be a random matrix in the orthogonal group $\O_n$, distributed according to Haar measure, and let $A$ be a fixed $n\times n$ matrix over $\R$ such that $\tr(AA^t)=n$. Then the total variation distance of the random variable…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a…
The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
We construct a continuous family of exchangeable pairs by perturbing the random variable through diffusion processes on manifold in order to apply Stein method to certain geometric settings. We compare our perturbation by diffusion method…
Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Building on the rather large literature concerning the regularity of the solution of the standard normal Stein equation, we provide a complete description of the best possible uniform bounds for the derivatives of the solution of the…
Consider a uniformly chosen random reduced decomposition of the longest element in the symmetric group. It is known that the location of the first transposition in this decomposition converges to the semicircle distribution. In this note we…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…
We propose a measure of the impact of any two choices of prior distributions by quantifying the Wasserstein distance between the respective resulting posterior distributions at any fixed sample size. We illustrate this measure on the…